Let \(M\)  be a hyperkähler manifold, that is, a compact,
holomorphically symplectic Kähler manifold. We assume that
\(\pi _1(M)=0\)  and \(H^{2,0}(M)={C}\) : the general case reduces to this by Bogomolov decomposition
(REF ). Such hyperkähler manifolds
are known as simple hyperkähler manifolds, or IHS (irreducible holomorphic symplectic) manifolds.
The known examples of such manifolds are
deformations of punctual Hilbert scheme of K3 surfaces, deformations of
generalized Kummer
varieties and two sporadic ones discovered by O'Grady.
In [1]} we gave a description of the Kähler cone
of \(M\)  in terms of a set of cohomology classes \(S\subset H^2(M,{Z})\) 
called MBM classes (REF ). This set is of topological
nature, that is, it depends only on the deformation type of \(M\) .
